The Game Theory and Long Run Marginal Cost in Microeconomics - Term Paper Example

This paper describes the game theory and long run marginal cost in microeconomics. This paper is divided into two parts and is structured in such a manner it explains the game theory on long-run average total cost and long run marginal cost. The first part of this paper involves the game theory approach and its implications on long-run average total cost. In many business situations, two or more decision makers simultaneously choose an action and the action chosen by each affects the rewards earned by the others. Few examples are supermarket pricing policy, employers and unions in wage negotiations. The mathematical analysis of these situations is called game theory and was originally developed by Von Neumann and Morgenstern in 1944. As the subject develops, it has gained acceptance, particularly in business, politics and with the military. In 1994 the Nobel Prize for Economics was awarded to Harsanyi, Nash and Selten for their contributions to Game Theory. The second part of the paper involves the study of the long run marginal cost. The long-run marginal cost curve indicates the change in total cost resulting from a change in production when all inputs including capital and plant size are variable. This paper discusses the different cases of long run cost curve with the categories of returns to scale. Keywords: Game theory, Marginal Cost (MC), Long-run Marginal Cost (LRMC). Game Theory: Here we only consider two person’s zero sum games. These are games with two players normally called A and B where in any play of the game the amount of As gain equals the amount of Bs loss (so the sum of both players gains is zero). We refer to As gain and Bs loss throughout the theory but naturally B can win games so As "gain" is not always positive. Our object is to find the best strategy for each player. By a "best strategy" we mean that if A (say) deviates from this strategy then B can adapt Bs strategy to gain more than if A stuck to the best strategy. Solving Simple Games Pure Strategies: To solve the game we first of all look for a pure strategy. This occurs when the best strategy for each player is to choose the same option for all plays of the game. If there is a pure strategy, A plays i and B plays j (say), then the ijth element (the payoff to A per play) is called a saddle point. To find whether a game has a saddle point we adopt the following procedure: 1. After each row place the smallest number in that row and ring the largest of these numbers. (This represents As minimum gain if A always played the same strategy) 2. Below each column place the largest number in that column and ring the smallest of these. (This represents Bs maximum loss if B always played the same strategy). Mixed Strategies and Dominance: If there is no pure strategy then we look for a mixed strategy which means each player mixes their options in certain proportions. Solving the game means determining these proportions in this case. The rules for simple dominance are as follows. 1. If all the elements in one row are less than or equal to the corresponding elements in another row then the first row is dominated and can be eliminated from the matrix. (A never gains more playing the first row rather than the second whatever B plays) 2. If all the elements in one column are greater than the corresponding elements in another column then the first column is dominated and can be eliminated from the matrix. (B never loses less playing the first column rather than the second whatever A plays) 3. Repeat steps 1 and 2 until no more rows or columns can be removed. Game Theory in Telecommunication: “Most optimization based approaches in telecommunication networks find the optimal MAC and routing parameters that optimize network throughput, lifetime, delay etc and assume all nodes in the network use these parameters. But there is no reason to believe that nodes will adhere to the actions that optimize network performance. Cheaters may deviate in order to increase their pay-offs which in turn effects other users. Game theory helps to capture this interaction, the effect of actions of rational players on the performance of the network. Player 1 wants to send a packet to r1 using player 2. Player 2 wants to send a packet to r2 using player 1. Cost of forwarding a packet equals c where 0 < c < 1. If packets get through to intended receiver, the sender gets reward 1. Possible actions are Drop (D) or Forward (F). Although (F, F) leads to better payoffs, (D, D) is the solution of the game.” (N.Bisnik, Pg. 9) Game Theory in Oligopoly: Oligopolistic firms have pricing discretion, but are interdependent. So they must always consider the reactions of other firms when making pricing or output-level decisions. “Example: Pepsi raises the price of its product: If Coke will also raise its price, both firms will benefit. If Coke does not raise its price, then Coke will benefit and Pepsi will suffer. Pepsi lowers the price of its product: If Coke will also lower its price, both firms will lose. If Coke does not lower its price, then Pepsi will benefit and Coke will suffer”. (Angela, Pg. 4) Thus, game theory studies the strategies employed by interdependent firms. These strategies are evaluated with payoff-matrix. Firm behavior in an Oligopoly: Game Theory is shown as a payoff matrix that shows the effects on both firms due to the actions of each individual firm. The Game Theory shows Mutual interdependence of firms: Firms in an oligopoly are interdependent on each other and one firms actions can affect another firm. Collusive Tendencies: Because of the benefits that usually arise when firms choose the worse outcome individually for them, there is the tendency to collude with the other firms so that they also choose this outcome. By choosing these, both firms can ultimately benefit in the end with higher profits. Incentive to Cheat: Following collusion, any one of the two firms can change its strategy and hence, benefit itself at the expense of the other firm. However, most firms try not to do this for the fear of retribution by the other firm. Long Run Marginal Cost (LRMC): Before getting into LRMC, it is required to know about the marginal cost which is the change in total cost that arises when the quantity produced changes by one unit. The marginal cost (MC) function is expressed as the derivative of the total cost (TC) function with respect to quantity (Q). Generally, marginal cost at each level of production includes the additional costs incurred to produce the next unit. In practice, the analysis is segregated into short and long-run cases and over the longest run, all costs are marginal. At each level of production and time period being considered, marginal costs include all costs which vary with the level of production and other costs are considered fixed costs. “Marginal cost can be estimated in either a long-run (LRMC) or a short-run (SRMC) perspective. The fundamental difference between SRMC and LRMC is the time frame under consideration and the implications for a firm’s ability to adjust its production process to minimize costs.” (Marsden, Pg. 11) The LRMC is the long-run marginal cost curve. This indicates the change in total cost resulting from a change in production when all inputs, including capital and plant size, are variable. In the long run none of the inputs to production are fixed. The shape of the long run cost curves depend on returns to scale. Returns to scale refers to the change in output when all factors are increased by the same proportion. The three kinds of returns are Increasing Returns (Ralitza Dimova, Pg. 19) to scale means that when all factors are increased by the same proportion, the total product increases more than proportionately (%  output > %  all inputs). If all inputs double, then output more than doubles. Average costs falls as output increases, they are slightly downward sloping but will level off. Therefore, bigger is better for firms facing increasing returns to scale. Constant Returns (Ralitza Dimova, Pg. 19) to scale means that when the production scale increases, the total product increases proportionately. The long run average cost curve is flat. If all inputs double, TC doubles and the output Q also doubles. Therefore, Average Cost (AC) stays constant, AC = Total cost (TC)/Q = (2TC)/(2Q). The constant average cost in the long run means that long run marginal cost must be constant and equal to long run average cost. If marginal cost was not constant, average cost would be changing. Constant returns to scale are prevalent in manufacturing. Decreasing Returns to scale (Ralitza Dimova, Pg. 19) means that when the production scale increases, the total product increases less than proportionately. If all inputs double then output increases by less than double. Average costs increase as output increases, in other words the long run average cost curve is upward sloping. Firms with decreasing returns to scale are more efficient at low levels of output and typically stay small. In this case the long run marginal cost curve is upward sloping and sits above the long run average cost curve. Bibliography 1. N. Bisnik. Game Theory and Communication Networks. http://www.cs.rpi.edu/~isler/teaching/fall06/presentations/gameTheory.pdf 2006. Page 9. 2. Angela. Industry Structure and Public Policy. http://faculty.clintoncc.suny.edu/faculty/Angela.Barnaby/ECO%20100%20slides%20in%20pdf%20format/Chapter%208%20Lecture%20Notes.pdf 2005. Page 4. 3. Ralitza Dimova. Cost and Supply. http://ralitzadimova.net/Lecture4_2008_09.ppt 2008. Page 19. 4. Marsden Jacob. Estimation of Long Run Marginal Cost http://www.qca.org.au/files/QCALRMCFinal.pdf 2004. Page 11. Read More